Error Estimates for systems of nonlocal balance laws modeling dense multilane vehicular traffic (2312.16928v3)

Abstract: We discuss a class of coupled system of nonlocal nonlinear balance laws modeling multilane traffic, with the nonlocality present in both convective and source terms. The uniqueness and existence of the entropy solution is proven via doubling of the variables arguments and convergent finite volume approximations, respectively. The primary goal is to establish that the finite volume numerical approximations of the system converge to the unique entropy solution at a rate of $\sqrt{\Delta t}$, even when using relatively less regular one-sided kernels, as opposed to the globally smooth kernels analyzed in [Num. Math., 156(1):237-271, 2024] and [IMA J. Numer. Anal., drad101, 2024]. The applicability of the proven theory to a general class of systems of nonlocal balance laws coupled strongly through the convective part and weakly through the source part, is also indicated. Numerical simulations illustrating the theory and the behavior of the entropy solution as the support of the kernel goes to zero (nonlocal to local limit), are shown.